A representation of Galois dual codes of algebraic geometry codes via Weil differentials

Galois dual codes are a generalization of Euclidean dual codes and Hermitian dual codes. We show that the h -Galois dual code of an algebraic geometry code C_ \calL,F(D,G) from function field F/ \mathbbF_p^e can be represented as an algebraic geometry code C_\varOmega,F'(\phi_h(D),\phi_h(G)) from an associated function field F'/ \mathbbF_p^e with an isomorphism \phi_h:F\rightarrow F' satisfying \phi_h(a) = a^p^e-h for all a\in \mathbbF_p^e . As an application of this result, we construct a family of h-Galois linear complementary dual maximum distance separable codes (h-Galois LCD MDS codes).